M2011861 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	14.7694	68.6567%	500000	15000000	0.1230	5.1267%	14.8924	70.2636%	1.6069%
PrimeNet	2⁵⁸	0.0191	63.7931%	9000	150000	0.0016	2.6100%	0.0207	64.7381%	0.9450%
GPU72	2⁶²	0.3054	66.1290%	8000	120000	0.0013	1.2722%	0.3067	66.5599%	0.4309%
Difference	+5	+14.4640	+2.5277%	+492000	+14880000	+0.1216	+3.8545%	+14.5856	+3.7036%	+3.7036%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7694

68.6567%

500000

15000000

0.1230

5.1267%

14.8924

70.2636%

1.6069%

PrimeNet

2⁵⁸

0.0191

63.7931%

9000

150000

0.0016

2.6100%

0.0207

64.7381%

0.9450%

GPU72

2⁶²

0.3054

66.1290%

8000

120000

0.0013

1.2722%

0.3067

66.5599%

0.4309%

Difference

+14.4640

+2.5277%

+492000

+14880000

+0.1216

+3.8545%

+14.5856

+3.7036%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2011861	3701824241	10	31.786	920 2³ × 5 × 23	-	8	23	1.705e-10	8.406e-7	1.552e-6
2011861	795630669671	12	39.533	197735 5 × 71 × 557	2008-07-15	71	557	6.552e-8	9.293e-6	1.378e-5
2011861	12077535551927	14	43.457	3001583 13 × 230891	2008-08-26	13	230891	9.862e-7	0.0012	0.0022
2011861	5974551496461980561	19	62.374	1484832077480 2³ × 5 × 29 × 3259 × 392767	2016-01-21	3259	392767	0.5800	0.0023	0.0038

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2011861

3701824241

31.786

920
2³ × 5 × 23

1.705e-10

8.406e-7

1.552e-6

2011861

795630669671

39.533

197735
5 × 71 × 557

2008-07-15

557

6.552e-8

9.293e-6

1.378e-5

2011861

12077535551927

43.457

3001583
13 × 230891

2008-08-26

230891

9.862e-7

0.0012

0.0022

2011861

5974551496461980561

62.374

1484832077480
2³ × 5 × 29 × 3259 × 392767

2016-01-21

3259

392767

0.5800

0.0023

0.0038

exponent	prime factors	composite factor	digits	bits*
2011861	3701824241 795630669671	2945284899871171294711	22	71.319
2011861	3701824241 12077535551927	44708913877662682862407	23	75.243
2011861	795630669671 12077535551927	9609257699154989604506017	25	82.991
2011861	3701824241 5974551496461980561	22116739558705785375580579201	29	94.159
2011861	795630669671 5974551496461980561	4753536408113920780939414265431	31	101.907
2011861	12077535551927 5974551496461980561	72157858105338230182568680091047	32	105.831
2011861	3701824241 795630669671 12077535551927	35571783088747825734063376560958097	35	114.776
2011861	3701824241 795630669671 5974551496461980561	17596756306032181036435174480113684112871	41	133.692
2011861	3701824241 12077535551927 5974551496461980561	267115708312979391993870595608411871670327	42	137.617
2011861	795630669671 12077535551927 5974551496461980561	57411004966375251340115063531790289861535537	44	145.364
2011861	3701824241 795630669671 12077535551927 5974551496461980561	21252544988469929531330567791123636913784878434955 2417	54	177.150

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-01-21T18:00:04	alpertron	Manual testing	500000	15000000	12		5974551496461980561	19	62.374	0.048	0.265	0.095	5.127%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	12077535551927	43.457	14	4.03804e-7	0.288	8.78505e-7
2008-07-15T07:49:00	J Feitsma	Manual testing	?	?	795630669671	39.533	12	2.91144e-8	0.288	6.33407e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.732 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.732 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.644	19.316%
25	50000	0.152	85.886%
30	250000	0.010	99.040%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	20	1.693
50000	6698861	7	0.674
50000	6750000	7	0.676
50000	7000000	7	0.688

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-26T18:12:34	Oliver Kruse	ECM-HTC	50000	5000000						3	0.254
2019-05-16T22:24:39	ATH	ec2-ECMCF	50000	5000000						3	0.254
2021-04-27T17:34:50	Poao	justg-ZA	50000	5000000						7	0.593
2021-08-06T03:51:24	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593
2021-10-27T01:07:51	Dylan Delgado	colab	50000	6750000						7	0.676
2022-03-22T18:25:58	happy5214	Focus	50000	7000000						7	0.688
2022-06-22T18:17:02	debrouxl	z400	50000	6698861						7	0.674

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:33:32

alpertron

Manual testing

3701824241

795630669671

12077535551927

5974551496461980561

FF0D8E6F317845__

2017-10-20T19:25:16

Oliver Kruse

Threadripper

3701824241

795630669671

12077535551927

5974551496461980561

FF0D8E6F317845__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront